The action of a few permutations on r-tuples is quickly transitive

Random Structures and Algorithms

Volumn 12, Issue 4, 1998, Pages 335-350

  Friedman, Joel ^a   Joux, Antoine ^d   Roichman, Yuval ^b   Stern, Jacques ^c   Tillich, Jean Pierre ^d  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c ECOLE NORMALE SUPÉRIEURE   (France)

^d NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032337421     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199807)12:4<335::AID-RSA2>3.0.CO;2-U     Document Type: Article

References (25)

1. D. Angluin, On the complexity of minimum inference of regular sets, Inform. and Control, 39, 302-320 (1978).
2. D. Angluin and C. H. Smith, Inductive inference, theory and methods, Comput. Surveys, 15(3), 237-269 (1983).
3. 1, isoperimetric inequalities for graphs and superconcentrators, J. Combin. Theory Ser. B, 38, 73-88 (1985).
4. L. Babai, Transparent proofs and limits to approximation, preprint, 1994.
5. L. Babai, G. Hetyei, W. M. Kantor, A. Lubotzky, and A. Seres, On the diameter of finite groups, Thirty-First Annual Symposium on Foundations of Computer Science, pp. 857-865, 1990.
6. B. Bollobas, Random Graphs, Academic Press, London, 1985.
7. B. Bollobas, The isoperimetric number of random regular graphs, European J. Combin., 9, 241-244 (1988).
8. B. Bollobas and W. F. de la Vega, The diameter of random-regular graphs, Combinatorica, 2, 125-134 (1982).
9. A. Broder and E. Shamir, On the second eigenvalue of random regular graphs, Twenty-Eighth Annual Symposium on Foundations of Computer Science, pp. 286-294, 1987.
10. C. Delorme, Counting closed paths in trees, Technical Report No. 516, Laboratoire de recherche en informatique Orsay, University of Paris-Sud, Paris, Sept. 1989 (in French).
11. Y. Freund, M. Kearns, D. Ron, R. Rubinfeld, R. E. Schapire, and L. Sellie, Efficient learning of typical finite automata from random walks, Twenty-Fifth Symposium on the Theory of Computing, 1993, pp. 315-324.
12. J. Friedman, On the second eigenvalue and random walks in random d-regular graphs, Combinatorica, 11(4), 331-362 (1991).
13. J. Friedman, Some geometric aspects of graphs and their eigenfunctions, Duke Math. J., 69, 487-525 (1993).
14. E. M. Gold, Complexity of automaton identification from given data, Inform. and Control, 37, 302-320 (1978).
15. A. Joux, J. Stern, and J. P. Tillich, Inferring finite automata by queries of fixed length, Technical report of the Ecole Normale Supérieure.
16. A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, Progress in Mathematics, Birkhäuser, Basel, 1994, Vol. 125.
17. A. Lubotzky, Cayley graphs: eigenvalues, expanders and random walks, London Math. Soc. Lecture Notes Ser., 218 155-189 (1995).
18. B. McKay, The expected eigenvalue distribution of a large regular graph, Linear Algebra Appl., 40, 203-216 (1981).
19. M. Mihail, Conductance and convergence of Markov chains - a combinatorial treatment of expanders, Proceedings of the Thirtieth Annual Symposium on Foundations of Computer Science, 1989.
20. B. Mohar, Isoperimetric number of graphs, J. Combin. Theory Ser. B, 274-291 (1989).
21. R. L. Rivest and R. E. Schapire, Diversity based inference of finite automata, Proceedings of the Twenty-Eighth Annual Symposium on the Foundations of Computer Science, 1987, pp. 78-87.
22. R. L. Rivest and R. E. Schapire, Inference of finite automata using homing sequences, Proceedings of the Twenty-First Symposium on the Theory of Computing, 1989, pp. 411-420.
23. J. P. Tillich and G. Zémor, Group-theoretic hash functions, in Proceedings of the First French-Israeli Workship in Algebraic Coding 1993, Lecture Notes in Computer Science, Springer-Verlag, Berlin/New York, Vol. 781, pp. 90-110.
24. U. Vazirani, Rapidly mixing markov chains, Proc. Sympos. Appl. Math., 44, 99-121 (1991).
25. G. Zémor, Hash functions and Cayley graphs, Design, Codes and Cryptography, to appear.